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<p>This article explores the chaotic dynamics of a hyperchaotic Lorenz system within the framework of fractional-order calculus, employing the Caputo derivative. The equilibrium point stability is analyzed using local stability theory, offering deeper insights into its dynamic behavior. Key analytical tools, such as phase portraits, time series, bifurcation diagrams, Lyapunov exponents, 0-1 tests, and Poincaré maps, are used further to investigate the dynamic properties of the new system. The system can produce periodic attractors of varying periods and chaotic attractors of diverse forms. A backstepping control strategy is proposed to achieve synchronization of a fractional-order hyperchaotic Lorenz system. Additionally, the effectiveness of the designed Radial Basis Function Neural Network (RBFNN) is validated through Root Mean Square Error (RMSE) metrics and extensive error analysis. This research introduces an innovative methodology integrating artificial intelligence to model and analyze fractional-order hyperchaotic dynamical systems, providing significant insights for future advancements in this field.</p>

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Dynamical analysis of novel fractional-order hyperchaotic Lorenz system with backstepping synchronous control and RBF neural network

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • M. G. Abbas Malik,
  • Muhammad Umar,
  • Zia Bashir

摘要

This article explores the chaotic dynamics of a hyperchaotic Lorenz system within the framework of fractional-order calculus, employing the Caputo derivative. The equilibrium point stability is analyzed using local stability theory, offering deeper insights into its dynamic behavior. Key analytical tools, such as phase portraits, time series, bifurcation diagrams, Lyapunov exponents, 0-1 tests, and Poincaré maps, are used further to investigate the dynamic properties of the new system. The system can produce periodic attractors of varying periods and chaotic attractors of diverse forms. A backstepping control strategy is proposed to achieve synchronization of a fractional-order hyperchaotic Lorenz system. Additionally, the effectiveness of the designed Radial Basis Function Neural Network (RBFNN) is validated through Root Mean Square Error (RMSE) metrics and extensive error analysis. This research introduces an innovative methodology integrating artificial intelligence to model and analyze fractional-order hyperchaotic dynamical systems, providing significant insights for future advancements in this field.